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The rectilinear Steiner tree problem is an NP- complete problem with many important applications in networks and very large scale integration (VLSI) design. This book examines the rectilinear Steiner tree problem and proposes sequential and parallel branch and cut algorithms to solve it. In this book, we present two new LP constraints: cutsec constraints and strong incompatibility constraints allow us to greatly reduce the time to solve the problem. We also present a message passing parallel algorithm to solve large problem instances in an heterogenous computing environment.